Hexa-fun

Geometry Level 3

A regular hexagon of maximum possible area is cut off from an equilateral triangle .The ratio of area of triangle to the area of hexagon is:

\dfrac{\sqrt{6}}{4}

\dfrac{3}{\sqrt{2}}

\sqrt{\dfrac{3}{2}}

\dfrac{3}{2}

1 solution

Chew-Seong Cheong
Dec 2, 2015

The largest regular hexagon possible inscribed in a equilateral triangle is shown below:

The figure shows that the regular hexagon is made up of $6$ small equilateral triangles of equal area and the equilateral triangle, $9$ . Therefore, the ratio of area of triangle to that of the hexagon $= \dfrac{9}{6} = \boxed{\dfrac{3}{2}}$ .

Hexa-fun

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